The Attractor-Cycle Notation for Finite Transformations

Abstract

We describe a new notation for finite transformations. This attractor-cycle notation extends the orbit-cycle notation for permutations and builds upon existing transformation notations. How the basins of attraction of a finite transformation flow into permuted orbit cycles is visible from the notation. It gives insight into the structure of transformations and reduces the length of expressions without increasing the number of types of symbols.

arXiv comment8 pages, 4 figures, this final version is implemented in SgpDec http://gap-packages.github.io/sgpdec/